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Regularization of the Kepler Problem on the Three-sphere

Published online by Cambridge University Press:  20 November 2018

Shengda Hu  and
Manuele Santoprete
Shengda Hu
Affiliation:
Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5. e-mail: shu@wlu.ca msantopr@wlu.ca
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Abstract

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In this paper we regularize the Kepler problem on ${{S}^{3}}$ in several different ways. First, we perform a Moser-type regularization. Then, we adapt the Ligon–Schaaf regularization to our problem. Finally, we show that the Moser regularization and the Ligon–Schaaf map we obtained can be understood as the composition of the corresponding maps for the Kepler problem in Euclidean space and the gnomonic transformation.

Keywords

70FxxKepler problem on the sphereLigon-Shaaf regularizationgeodesic flow on the sphere
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 66 , Issue 4 , 01 August 2014 , pp. 760 - 782
Copyright
Copyright © Canadian Mathematical Society 2014

Footnotes

*

The research of S. H. was supported by an NSERC Discovery Grant and a Wilfrid Laurier start-up grant. The research of M. S. was supported by NSERC through a Discovery Grant.

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